This paper investigates the problem of controlling half-vehicle semi-active suspension system involving a magnetor-heological (MR) damper. This features a hysteretic behavior that is presently captured through the nonlinear Bouc-Wen model. The control objective is to regulate well the heave and the pitch motions of the chassis despite the road irregularities. The difficulty of the control problem lies in the nonlinearity of the system model, the uncertainty of some of its parameters, and the inaccessibility to measurements of the hysteresis internal state variables. Using Lyapunov control design tools, we design two observers to get online estimates of the hysteresis internal states and a stabilizing adaptive state-feedback regulator. The whole adaptive controller is formally shown to meet the desired control objectives. This theoretical result is confirmed by several simulations demonstrating the supremacy of the latter compared to the skyhook control and passive suspension.